In a party of 35 people shake hand with everyone?

Answer 1

595 If you have 35 people and everyone shakes hands with everone else, you have 35x34/2 total handshakes. To see this think of three people, and fix one of them, say it's you! You shake hands with everyone meaning you shake hands with 2 people And each of them shakes hands with each other, that is two people other than you so the total 2+1= 3 which is 3x2/2 Try it with 4, you shake hand with 3 people, and they all shake hands with each other so we have your 3 plus 3 more. To see the three more, just look at what we just did above. 4x3/2=6, We divide by 2 to avoid double counting. Because you shake hands with me and I shake hands with you, but we only shake hands once, so divide the total by 2. In general for n people at a party, we have n(n-1)/2handshakes.